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# Math

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Stefania’s parents calculate that they will need \$7500 every 3 months for 4 years to pay for Stefania’s college. They have 18 years until she is college age. How much should they invest every 3 months at 6.4%/a compounded quarterly for the next 18 years if they plan to withdraw \$7500 per quarter for the 4 years after that?

Julius  Jun 15, 2017
edited by Julius  Jun 16, 2017
#1
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The Future Value of Stephania's college fund will be =\$106,817.02. To save this amount over a period of 18 years or 72 quarters @ 6.4% compounded quarterly, they will need to invest =\$787.60 at the beginning of each quarter for 18 years or 72 quarters.

P.S. Do you know or understand the TVM formulas used to calculate these amounts? If you don't, then let us know here and will explain them to you.

Guest Jun 15, 2017
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I have all the formula's, but I don't understand how you got the future value

Julius  Jun 15, 2017
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From the point of view of Stefania, it is Present Value of \$7,500 quarterly payments, or 16 payments of \$7,500 each. For that purpose, you will use this formula:

PV=P{[1 + R]^N - 1.[1 + R]^-N} R^-1 x [1 + R]

PV =7,500 {[1 + 0.064/4]^(4*4) - 1 / [1 + 0.064/4]^(4*4) / (0.064/4)} x [1 + 0.064/4]

PV =7,500{[1.016]^16 -1 / [1.016]^16 / 0.016} x 1.016

PV =7,500 x                     14.01798181......             x 1.016

PV =\$106,817.02 - This is the PV of Stefania's payments, But it is the Future Value from the point of view of her parents. In other words, this is the amount they must have in future for their daughter's quarterly withdrawals. So, how much do the parents need to invest each quarter to have this amount in 18 years, or 18 x 4 = 72 quarters?

To find that out, you have to use this formula:

FV=P{[1 + R]^N - 1/ R} x [1 + R]

\$106,817.02 =PMT {[1 + 0.064/4]^(18*4) - 1 / (0.064/4)} x [1 + 0.064/4]

\$106,817.02 =PMT{[1.016]^72 -1 / 0.016} x 1.016

\$106,817.02 =PMT x              135.622666.......

PMT =\$106,817.02 / 135.622666....

PMT =\$787.60 - This is the quarterly payment that her parents must invest at the beginning of each quarter for 18 years or 72 quarters @ 6.4% compounded quarterly.

Guest Jun 15, 2017